Suppose A is any 3 3 non-singular matrix and ( A -3 I )( A -5 I )=0 where I = I ₃ and O = O ₃ . Here O ₃ represent zero matrix of order 3 and I ₃ is an identity matrix of order 3 . If A + A ⁻¹=4 I , then + is equal to

Step-by-step solution

array ll & Given that (A-3 I)(A-5 I)=0 & A^2-3 A-5 A+15 I=0 & A^2-8 A+15 I=0 & A^2+15 I=8 A array Multiplying entire equation by A⁻¹ 2 , we get 1 2 A+ 15 2 A⁻¹=4 I Comparing with A + A ⁻¹=4 I , we get aligned & = 1 2 and = 15 2 & + = 1 2 + 15 2 =8 aligned